Unified analysis of pion single- and double-charge-exchange scattering in the resonance region

We present the results of a phenomenological analysis of all existing data on pion single- and double-charge-exchange scattering to isobaric analog states at $T_{\pi }\simeq 164$ MeV. We use a theory in which both reactions are described by the same optical potential, $U$. The form of $U$ is theoretically motivated and separates explicitly the effects of nuclear structure and reaction dynamics. The latter is characterized phenomenologically by two complex numbers, one for the isovector and one for the isotensor term in $U$. Elastic scattering from selected $N=Z$ nuclei is independently fitted to determine the isoscalar terms in $U$. Realistic Skyrme III densities are used to describe the nuclear structure. We find one set of parameters which describes the scattering throughout the periodic table. The striking $N$, $Z$, and $A$ dependence predicted by the lowest-order $U$ and observed in the data is preserved.